Abstract
Bayes’ rule provides a method for constructing estimators of probability density functions in both parametric and nonparametric cases. Let X 1, X 2, ..., X n be a random sample from an unknown probability measure P 0 with density function p 0(x) with respect to a dominating measure λ(dx). Let µ be a prior probability measure on the space of all probability measures P which have densities p(x) = dP/dλ. Then the mean of the posterior yields the following estimator of the density function
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
I. Csiszár, “Information-type Measures of Difference of Probability Distributions and Indirect Observations,” Studia Sci. Math. Hungar. 2, pp. 299–318 (1967).
J.L. Doob, “Application of the Theory of Martingales,” Colloq. Int. CNRS, pp. 22–28 (1949).
A.R. Barron, “Discussion on the Consistency of Bayes Estimates,” Ann. Statistics, 14, pp. 26–30 (1986).
L. Schwartz, “On Bayes’ Procedures,” Z. Wahrsch. verw. Gebiete, 4, pp. 10–26 (1965).
D. Freedman, “On the Asymptotic Behavior of Bayes Estimates in the Discrete Case,” Ann. Math. Statistics, 34, pp. 1386–1403 (1963).
H. Strasser, “Consistency of Maximum Likelihood and Bayes Estimates,” Ann. Statistics, 9, pp. 1107–1113 (1981).
A.R. Barron, “On Uniformly Powerful Tests and Bayes Consistency,” in preparation.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Barron, A.R. (1987). Are Bayes Rules Consistent in Information?. In: Cover, T.M., Gopinath, B. (eds) Open Problems in Communication and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4808-8_22
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4808-8_22
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-9162-6
Online ISBN: 978-1-4612-4808-8
eBook Packages: Springer Book Archive